I must profess to not knowing too much about either lens, though they sound quite similar in spec...if upgrading lenses, I'd be tempted to look for a faster aperture or a longer reach - much depends on what you need.
Same goes for the body - the A580 will be a significant step up in some regards over the A200, but probably not too different in daylight IQ. So if you mostly shoot good daylight wildlife, it might not have a huge impact. However, shoot in mixed light, need higher ISOs, want faster burst, want live view option for off angles, or need to track moving subjects, and the A580 becomes quite a significant step up over your current cam.
Sony DSLR-A68 / Sony 18-250mm / Minolta 50mm F1.7 / Tamron 150-600mm / Minolta 300mm F4 APO
Sony A6300 / 18-55mm F3.5-5.6 / 55-210mm F4-6.3 / 10-18mm F4 / 35mm F1.8 / 16mm F2.8 / FE70-200mm F4 G OSS / FE70-300mm F4.5-5.6 G OSS / via manual adapter, lots of Pentax K mount, Konica K/AR mount, and Leica M mount manual lenses