Moto X: 8 to 9 hours (browsing, Wi-Fi), 13 to 14 hours (talking, 3G), 13.8 days (standby). "Up to 24 hours," Motorola claims.
iPhone 5S: 8 megapixels, f/2.2 aperture. LED flash. Digital image stabilization, backside illumination sensor, five-element lens, 3X zoom.
Moto X: 10 megapixels, f/2.4 aperture. LED flash. Digital image stabilization. 4X zoom.
iPhone 5S: 1.2 megapixels at 1280-by-960-pixel resolution. Backside illumination sensor.
Moto X: 2 megapixels at 1600-by-1200-pixel resolution.
iPhone 5S: gold, gray, silver
Moto X: black ("woven" texture), white ("woven" texture). Sixteen additional flat colors available via "Moto Maker" customization process.
iPhone 5S: Uses iTunes Store for downloadable music; no terrestrial radio support. Supports AAC, Protected AAC, HE-AAC, MP3, MP3 VBR, Audible (formats 2, 3, 4, Audible Enhanced Audio, AAX, and AAX+), Apple Lossless, AIFF, and WAV file formats for playback.
Moto X: Uses Google Play Store for downloadable music; no terrestrial radio support. Supports AAC, AAC+, eAAC+, FLAC, MP3, WMA, WAV, AMR, OGG and MIDI file formats.
iPhone 5S: Records at up to 1080p (Full HD, 1920-by-1080-pixel resolution) at 60 frames per second. 3X video zoom. Supports H.264, MPEG-4, M-JPEG, as well as FaceTime video calling with similarly enabled devices; AirPlay mirroring and video out to Apple TV, video mirroring with adapter. Includes slow-motion video capability, video stabilization, face detection, geotagging and ability to take still photo while recording.
Moto X: Records at up to 1080p (Full HD, 1920-by-1080-pixel resolution) at 60 frames per second. 4X digital zoom. Supports MPEG4, H.263, H.264. Includes slow-motion video capability, face detection, geotagging.
iPhone 5S: Unknown
Moto X: 2 gigabytes.
iPhone 5S: 16, 32 or 64 gigabytes local; 5 gigabytes free in the cloud
Moto X: 16 or 32 gigabytes local; 15 gigabytes free in the cloud (plus an additional 50 gigabytes, free for two years)
iPhone 5S: Apple A7 (dual-core, 1.7 GHz)
Moto X: Qualcomm Snapdragon S4 Pro (dual-core, 1.7 GHz)
iPhone 5S: Nano SIM (storage); Lightning (charging); 3.5 mm audio. USB, Bluetooth 4.0, 802.11 a/b/g/n Wi-Fi.
Moto X: Nano SIM (storage); micro USB (charging); 3.5 mm audio. USB 2.0, Bluetooth 4.0 EDR, 802.11 a/b/g/n/ac Wi-Fi.
iPhone 5S: Fingerprint sensor, slow-motion video capture, OpenGL ES version 3.0 support for higher-res gaming, free iWork apps.
Moto X: Touch-less/voice-activated control; wrist-flick camera activation; Motorola Assist intelligent shortcut tool; Motorola Connect in-browser communication tool for Chrome. Oh, and all those colors.
This list can't be everything to everyone, but if you're interested in more specifications or features that are not included here, visit the detailed product page for the iPhone 5S. (There isn't an official one available for the Moto X.) If we've missed anything major, just give us a shout.