I'm pretty new to audio coding technology and especially to AAC encoding technique.

I did encode several PCM-based tracks (mostly Microsoft WAVE format) with Psytel 2.15 AAC Encoder.

how does it come it takes so much time to encode a file whereas it's just a question of seconds with MP3 encoder from Fraunhofer ?

Does this problem come from the technology diferences between MPEG-2 Layer III and MPEG-4 AAC or is this a question of software implementation ?

This is a very wrong comparison .. That's just what that Fraunhofer encoder is, an MP3 encoder, not an AAC encoder.
I wouldn't call it a "problem".. Oh and it's "MP3G-1 Layer 3" you're talking about.
Technology differences. MPEG-4 AAC is a different technology, takes longer to encode. Ivan keeps optimising the encoder's speed, so probably it will be much faster in the future. (there won't be a newer AACEnc demo, Ivan now works at Ahead)

AACenc 2.15 takes longer because it's doing a better job

I think it's safe to say that at the same bitrate, AACenc will create a higher quality file than the Fraunhoffer MP3 encoder. It's more complex, and so takes more time at the moment.