Why just those two? Have you looked at Zoom & Line 6 and all the others that are out there?
Gibson LP Traditional, LP GT, LP Studio, SG Standard x2
Barber Tone Press > EHX Worm >TC Polytune > EXH Glove > EHX East River Drive > Zoom G3 > TC Spark Mini Booster
Jet City JCA22H
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Boss ME80 is new. AX3000G is ancient. If those two are the only choice I would get the Boss.
go boss. i have the 1500g from around a decade ago, at the time it wasn't bad, but in comparison to what you can get today, its trash. the only thing i liked was that it hat an odd pitch bend (with the pedal), ring mod was interested to.

but i have it lying around, but it will never near compete anything on the market today.

if you are low on cash, pick up a line 6 XT/X3/HD (from bad to good)
The Boss will work fine for you, bruh. As Gary mentioned, there are several decent mfx units in between the 2 (the Korg is almost the bottom of the barrel, the ME-80 is halfway up the barrel). The Zoom G3/G3x/G5 and the Line 6 M series are good, as is the Vox Tonelab.
Fender Mustang/Derfenstein DST> Boss Power Wah> Pedal Monsters Klone> Bogner Uberschall> Walrus Audio Janus> Randall RM20> Line 6 M9> Randall RM20
And can i get tones from famous songs on the boss??
If you want tones from famous songs then get the Tonelab EX. All the patches are based on and named for famous songs. Right in the Tonelab EX description...

"Includes 50 Song Presets that recreate the guitar sound used on well-known songs"