No real difference. As long as you sanitize the ferment vessel it shouldn't matter If you use the carboy or the bucket.
Just a few minor differences:
Carboys have smaller openings= less possibility for contamination but also more difficult to oxygenate the wort before you pitch your yeast.
- also if you plan to dry hop then you will have to rack your beer into the bucket if you are using a significant amount of whole leaf hops or even Pelletized hops
Carboys are typically transparent. Light penetration could have some adverse affects on some strains of yeast.
Carboys are nice because you can observe your kreusen as fermentation occurs,
But I always just use ferment buckets and plenty of sanny
MAINTAIN PROPER FERMENTATION TEMP RECOMMENDED FOR STRAIN OF YEAST.... Makes all the difference in final quality!
Best of luck in your first brew!