I am going to try to keep this short...
WAV and AIFF files SHOULD NOT play differently in any DAW. I do however, prefer AIFF since WAV file headers sometimes differ. AIFFs play on both Macs and PCs in all DAWs I know of.
The WAV specification includes some optional features. The optional fact chunk reports the number of samples for some compressed coding schemes
So... just use AIFF

I have been converting, importing, and exporting audio files from every possible DAW to another and never had any issues, there are, however, some things to remember when the different DAWs cannot open the project directly... here is a small checklist of rules
1) Make sure the source file is compatibleFor example, if you have true tape
32-bit files from Cubase VST 5 and move them into... say... a DAW like Logic on Mountain Lion, Logic will accept the files, But not play them since Logic only uses up to 24 Bit files, this can get very confusing to have files in the Media pool that don't play back or auto-convert as expected.
So to simplify, check bit depth compatibility first; then obviously check sample rate compatibility.
2) Convert all files (if needed) before the import: Use a batch converted (like the one in the Prosoniq SonicWORX PowerBundle v2.6 or Spark) that can covert all all your SOURCE files unattended from one format to another... this saves tons of time
3) One File per Track Rule: The exported files should be 1 file per track in the arrangement, DO NOT export segments of audio (for example 6 segments of vocals on the main vocal track); trying to import, order, and line up multiple audio files on a single track in the new DAW will be nearly an impossible task and usually take longer then re-recording
4) Dry Audio Rule: Unless you added some incredible effect that you cannot reproduce, the exported files should be all "dry" with NO effects. You have to learn the new DAW anyway, so apply effects there. they will not be removable from your exported audio.
5) Bar 1 (or zero) rule: It is a good practice to set start makers for ALL tracks from the Source DAW at the same bar before exporting; for example, if a chorus does not come in until bar 37... still set the marker with all the other tracks at the same start maker (usually 0 or 1). This will pad silence to the begging of all audio tracks (that start after the first bar) and it will also waste some hard drive space, but it makes it so much easier when dragging the files into an arrangement of a new DAW since you can line them all up at the begging of the song and they will all be in sync; you can then cut and delete regions to save space later.
6) Print all MIDI tracks that are NOT available in New DAW: Any virtual instruments that are unavailable in the new DAW should be turned into audio in the old DAW (remember, start maker at beginning of song regardless of when the MIDI track starts playing); this will give you the synth track you love in the new DAW in sync with all audio tracks. Also, it is usually a good idea to export 2 tracks of each virtual instrument if you spent mega-time with crazy in tempo applied effects, one with effects and one dry, this will give you maximum options in the new DAW
7) MIDI export/import before Audio extremely obvious; but mute all audio tracks and export the project as a standard MIDI file (type 1), and import as a standard MIDI file into the new DAW before working with the audio, this will give you your initial template with Tempo into the new DAW
WTF is Track 9 ?: Also extremely obvious, but never the case, try to use the clearest naming conventions on the source audio files (even if you have to rename them in the pool of the old DAW); this make things so much easier to re-essemble the project in the new DAW