I've got 6 budgies and 2 tiels( actually 4 but 2 are still in quaratine) they play together on the play gym and on the floor, all day every day,
They don't bother eachother, there is occasionally a snip from one of the tiels to one of the budgies but never any contact, The tiels sit on one end of the play gym and mind their bussiness and the budgies play ( i actually got video the other day of them all playing)
the only time my tiels get a little snippy is when tweety ( my budgie) does his/her Budgie Slide ( Tweety loves to slide back and forth on a perch any perh and the top perch of the play gym seems to be one of his/ her hot spots
as long as the budgies keep their distance there is no bickering on the play gym - - I haven't seen any bickering at all on the floor
but like what has already been mentioned, Its all about the birds personalities on how well they'll get along
I've heard of several people housing tiels and budgies together and never having a problem.... but in my opioion on that scenario I really think that would work best (if at all) when the budgies and tiels are raised together from the very start as babies, and that still isn't a garauntee
but as long as their play time is monitored with a watchful eye I see no problems