usually i'd recommend a workstation for playing in a band, but since it's for a 13-year old your choice seems good.
PSR is lightweight so your kid won't start cursing every time he needs to lift up his keyboard and carry it out to a gig or a rehearsal.
PSR e413 and e423 are basically the same keyboard where the e423 is the newer model.
I guess you can't even buy the e413 any more unless they still have it left in stock.
And if you are able to choose between the two models - go for the newer one - they cost the same
Also note one more thing - The PSR series is a series of arranger keyboards - meaning they have styles that can accompany you while playing.
Therefore - all arranger keyboards have very limited sound editing capabilities. You will be able to add and edit some effects like reverb and some filters
but that's about it.
Also, the PSR series allow layering of only 2 sounds at once and at a fixed split point, while workstations allow layering of 4, 8 or even up to 16 sounds at once
across all the keyboard at any split point and at different velocity levels.
But like I said - I don't think a 13year-old would like to have a massive-complex workstation in front of him at this early stage of playing.
Once he gets to love it - then be prepared to cash out A LOT of money for more and more and more keyboards hehe...
It's a disease!
