What "DAW" to use on iOS is just as an individual choice as is on your desktop or laptop.

I'd say I know all relevant iOS apps in this area and there's quite a choice like you said.
First off, bein on iPhone not iPad, your fun is going to be bery limited anyway because setting notes on such a tiny screen is more like a matter of hit-and-miss.

First two high-end DAWs:
BeatMaker 2 is not the latest but still a fantastically powerful app. If you take the time to learn using it (and you will need some time, promised ;-), you'll have an app than will even sync with your desktop DAW if you use AudioMux and MidiMux, it handles loops well, you can edit sounds in-app, you can build your own multi-velocity-layer sample instruments (no other iOS app can do this), and it comes with a choice of sounds good enough to have a grat start.
Caustic is another great app, can do a lot more than BM2 in the synth department but BM2 is better in the loops and samples department.
Caustic is pattern-oriented (remember The Orion DAW?) while BM2 is more like a conventional, linear DAW, although using loops on pads, you can jam along live and in sync with other gear or apps as well.

Some completely different and more intuitive concepts and great for composition on-the-go nonetheless (only a few highlights here):
- triqtraq: A very unique approach to composition, supports sample import, great, watch the videos...
- Xynthesizr: Probably the best alternative to the iPad-only Auxy app for sequencing chords, works in-sync with other apps, no samples but an internal synth
- LP-5: Loops and Breakbeats only, does sync and time stretching, with an interface that reminds Ableton
- energyXT: Formerly a desktop app, now on iOS too, quite powerful and simple to use, supports samples.
These four are ihmo all better replacements for figure without getting too complex, although without doubt, triqtraq is the deepest of them. I like it a lot.

DM1 is a great app for drums, but well, drums and single-hit samples only.

I'm hesitating to recommend NanoStudio. It is very nice to use but just too limited in many ways: No sync, only barebones and too limited sample support, no Midi Out etc.
You certainly heard of Cubasis too, but the sounds are imho its biggest weakness and decide for yourself if it's worth the high price.
Xewton Music Studio is another option to consider, its sounds are not the best but it supports user samples and hits a sweet spot between features and usability. And it has chord buttons (i.e. Chord Memory), especially useful on an iPhone!

Last but really not least, GarageBand!
Runs on iPhone, gives you a good and usable collection of sounds and again, is both powerful and easy to use.

Plenty of options...