Denise & Nancy can best answer this one - but i have to put my

worth in here too.
I think that many birds really do well in separate cages. Budgies are more active than most birds - almost finch like. From what Denise has said - the Linnie is more laid back & they are walkers so their cage set up should reflect that. 'Course my Budgies are walkers too - drat them!
If you have a really big cage maybe you can have the 2 together. You will probably play it by ear - I've never heard of a Linnie attacking anything.
I have 2 Budgies & 2 cages - cause the older one will not share his space & unlike yours they are males. Mine are out all the time & if you plan on having yours out as well i'm sure they will play together at least. Sarah has 2 Budgies & a Tiel that hang together - but separate cages otherwise.