i was just eyeing some phones a few hours ago, so lets discuss.
not to ruin the fun but lemme just drop a few comments, HTC J butterfly or Sony Xperia Z/ZL would've been a better candidate though, albeit more expensive.
the reason as to why to frown upon Nexus 4 is it's highly restrictive 16GB storage space limit(why oh why didn't they even try to push it to 64GB...).
HTC J Butterfly
Manufacturer HTC
Dimensions 143 mm (5.6 in) H
71 mm (2.8 in)W
9.1 mm (0.36 in) D[1]
Weight 140 g (4.9 oz) (HTC Droid DNA)[2]
Operating system Android 4.1 Jelly Bean[3]
SoC Snapdragon S4 Pro
CPU Quad-core 1.5 GHz "Krait" APQ8064 processor[4]
Memory 2 GB RAM[3]
Storage 16 GB internal[3]
Removable storage Expandable up to 32 GB with microSD (J Butterfly only)
Battery 2020 mAh[3]
Display 5 inch "Super LCD 3" display
1920×1080 pixels (441 ppi)[4]
Rear camera 8 MP, FullHD 1080p video recording at 30 FPS[3]
Front camera 2.1 MP, HD 720p video recording at 30 FPS[3]
Connectivity Bluetooth 4.0, WiFi, NFC, FeliCa, infrared[3]
Website http://www.htc.com/jp/smartphones/htl21
Sony Xperia Z (Sony C6603) Brand Sony
Manufacturer Sony Mobile
Slogan The Best of Sony in a Premium Smartphone [1]
Series Xperia
Compatible networks GSM/GPRS/EDGE 850/900/1800/1900
HSPA+ 850/900/2100
LTE 800/850/900/1800/2100/2600
First released February 9, 2013; 4 days ago
Availability by country February 9, 2013; 4 days ago (Japan)
Type Smartphone
Form factor Slate
Dimensions
139 mm (5.5 in) H
71 mm (2.8 in) W
7.9 mm (0.31 in) [2]
Weight 146 g (5.15 oz)
Operating system Android 4.1 Jelly Bean [2]
SoC Qualcomm Snapdragon S4 Pro APQ8064
CPU 1.5 GHz quad-core Krait
GPU Adreno 320
Memory 2 GB RAM[2]
Storage 16 GB
Removable storage up to 32 GB microSD/HC[1] card
Battery 2,400 mAh[3]
Data inputs Multi-touch, capacitive touchscreen, proximity sensor[1]
Display
5 in (130 mm) diagonal IPS
1920x1080 px (441 ppi)
Rear camera
13.1 MP back-side illuminated sensor with LED flash
1080p video recording @ 30 frames/s
Front camera 2.2 MP[1]
Connectivity
4G LTE(100 mbps)[1] GPS
GLONASS
Micro USB 2.0
Bluetooth 4.0
NFC
Wi-Fi (802.11 a/b/g/n)
DLNA
USB On-The-Go
MHL
Other
Available in black, purple and white
IP55, IP57 (Dust-proof & Water-resistant)
Nexus 4
Nexus 4
Brand Google/LG
Manufacturer LG Electronics
Series Google Nexus
Compatible networks
GSM/EDGE/GPRS (850, 900, 1800, 1900 MHz)
3G UMTS/HSPA+/DC-HSPA+ (850, 900, 1700, 1900, 2100 MHz)
HSDPA 42 Mbps
LTE band 4[1] (unofficially)
First released November 13, 2012; 2 months ago
Availability by country November 13, 2012 (Google Play)
Predecessor Galaxy Nexus
Related Optimus G
Nexus 7
Nexus 10
Type Smartphone
Form factor Slate
Dimensions
133.9 mm (5.27 in) H
68.7 mm (2.70 in) W
9.1 mm (0.36 in) [2]
Weight 139 g (4.9 oz)
Operating system Android 4.2.1 Jelly Bean
SoC Qualcomm Snapdragon S4 Pro APQ8064
CPU 1.5 GHz quad-core Krait
GPU Adreno 320
Memory 2 GB RAM
Storage 8/16 GB (depending on version)
Battery
3.8 V 2100 mAh, 8 Wh
rechargable Lithium polymer non-removable battery
Talk time 15 hours
Maximum Standby Time 390 hours[3]
Data inputs Multi-touch, capacitive touchscreen, proximity sensor
Display
4.7 in (120 mm) diagonal IPS with Corning Gorilla Glass 2
1280×768 px (320 ppi)
Rear camera
8 MP back-side illuminated sensor with LED flash
1080p video recording @ 30 frames/s
Front camera
1.3 MP
720p video recording @ frames/s
Connectivity
3.5 mm TRRS
GPS
GLONASS
Micro USB 2.0
Mobility DisplayPort (MyDP) [4]
Bluetooth 4.0 with A2DP [5]
NFC
Wi-Fi 802.11b/g/n (2.4/5 GHz)[6]
Qi Wireless Charging
Website Nexus 4
ok now that thats out:
Nexus 4's 1.5Ghz quad core krait should be able to handle 1080P Hi10P files at 25MB/minute(600MB per standard 24minute files).
(my phone can handle 10MB/minute 720P Hi10P and it merely has a dualcore A5 @ 1.2ghz which puts it at 3,768 score. QC-Krait @ 1.5Ghz has 19,800 score, now you can go figure

).
being able to decode 1080P isn't necessarily useless on a tiny screen since Nexus 4 has "Mobility DisplayPort (MyDP)" which you can use to output to a TV or monitor, but none the less the Nexus 4's screen has a resolution of 1280×768 and is able to output unscaled 720P. as for the resolution at that tiny screen, well you can read this article for that
http://www.cultofmac.com/173702/why-retina-isnt-enough-feature/possibly the reason why your playback was skippy is that you haven't installed MX Player ARMv7 Neon decoder yet, or the processor's frequency isn't maxed out at the moment of playback.
and/or you haven't set the proper settings in MX Player, it should be -
[under decoder settings]
H/W+ decoder [blank]
H/W+ decoder (local) [blank]
H/W+ decoder (network) [blank]
H/W+ decoder (10-bit) [blank]
correct aspect ratio [blank]
S/W decoder (local) [check]
S/W decoder (network) [check]
S/W audio [check]
CPU core limit [four]
color depth [16bit](set to 32bit if you think your phone can handle it, and your screen has the color capacity to do so)
Deinterlace [blank]
[under subtitle settings]
Enable subtitles [check]
Enable embedded subtitles [check]
H/W acceleration [blank]
notice that H/W decoding isn't being used, its because i noticed it once on my phone that not every encodes seems to be supported and it crashes MX Player plus the processor is plenty to software decode most of the files, otherwise you can play around with that.
MP3 shouldn't be an issue, thats weird, although which MP3 player are you using as that might be the culprit.
apps i suggest:
Airdroid (simply one of the most useful phone manager)
ALogCat (reads logs, its pretty much useless for most people though handy to have)
Battery+ (for battery indications, if you know a better app please share, i'm also searching for current(mA)charge rate indication app)
Camera ZOOM FX (got to say i've yet to see a better camera app out there)
ColorNote (sticky note, one of the easier to use out there)
CPU Identifier (its not only restricted to CPU-ID but can mostly identify the whole phone)
MX Player + MX Player ARMv7 Neon (SOP)
Opera Mobile (got no idea if firefox mobile is actually better than this, but opera's turbo works hell good)
Perfect Viewer (you know... manga viewer, can double as a picture viewer too)
poweramp (a good music player, quite good with playlist management as well)
quickpic (alternate picture/gallery viewer)
SetCPU (its a must, definitely a must)
Terminal (command-line ftw)
Titanium backup (should i say why?)