I've never actually used Backup Execs Transaction log backups, so I can't be certain, but I believe if you use it you can do point in time restores.
The solution I'd personally suggest that I use on our SQL servers is to use a combination of the two for the two types of restore you might want to perform.
I do a complete full backup including full SQL backup each night with Backup Exec for recovering in a disaster recovery situation, where I'll want to restore the entire server and all of the databases at once.
I then also do a SQL maintenance plan backup each night of all the databases, which then enables me to restore an individual database very quickly if required (eg when someone makes a mistake! :) I don't personally bother with transaction log backups during the day due to the nature of the data in use, but you could use it as well to allow you to restore to any point during the day.
To avoid the problem you mentioned with the tranaction logs I'd suggest making sure you're full backup part of the maintenance plan is performed after the Backup Exec job will have completed.
