Do both, linkage first, that will probably help this issue most, and of course it is real and not placebo.
If the gearbox oil is low topping it up will also help. - ETA: see also PipH's advice.
Then after you have confirmed how much the linkage adjustment has helped if your car is 15 years old and still with the original gear oil change it and get further improvements and better present and future protection. Buy very good quality oil as the extra cost isn't much, and it's normally a very easy job to do yourself, even I can do it, the better oil will make a difference and offer greater margins of protection which can be very useful on older vehicles.
You will get a real improvement, it was the first job I done on my wife's 6 year-old Mk3 at 38k-miles, she said she noticed the difference on gearchanges and we've been together far too long not to be honest about such things.
I've been told for years by mechanic-types that it makes no difference, and better oils are a waste of money, yet I have found both do. Just because oil been in the ground for millions of years some think that's how long it lasts in the gearbox when actually it starts to deteriorate quite quickly, yes it can last many, many years but it's not doing its job as well as it should (but perhaps good enough for some).
I always drain the existing oil as hot as possible and leave to drain for as long as possible to get as much of the existing oil and crud out as possible and so that the new fresh oil is less diluted by the existing oil and crud residue left in the box.
Dropping the gearbox oil also gives the chance to see if there are any metals bits in it, and to compare with the fresh new oil.
Of course changing to fresh better quality gearbox oil won't repair worn parts but can help and protect more and better than very old very worn oil.