Is there a way to get rid of the old enchant?

I have come across many enchanted items of the same sort.

For example Items of Sneak that increase sneak skill by different percentages.

Now throughout my game i think i have found out that when you disenchant an item of sneak, you cannot disenchant an iten of sneak with a higher enchant.

For example you disenchant early on in game an Armour of sneak +10%

Later on in game, you find another piece that has sneak skill +45% (may or may not be in game)

This item cannot be disenchanted due to already having that enchant just in a lower form,

Is there a way to get rid of the old or lower enchant and take the bigger and newer one?

This would be very useful for getting the best enchants in the game to place on other items that you personally like.

Or do you need to collect everything and then disenchant the best items first of all?

The magnitude of the effect on the item you disenchant does not impact the magnitude of the effect on items you enchant yourself. It depends entirely on your skill, the soul gem used and your enchanting perks.

So, given the choice between disenchanting an item of sneak 10% or sneak 45%, you could disenchant the item of sneak 10% to learn the fortify sneak enchantment and save the item of sneak 45% to either sell or keep. If you are trying to level your Enchanting skill you may wish to disenchant the equipment with the highest effect as this will give more exp.

It should be noted that there is one enchantment that has two versions, and that is the magic resist enchantment that the Shield of Solitude grants. It has a higher base magnitude than all other standard magic resist enchantments and it counts as a separate enchantment effect. In fact, if you had the extra effects perk, you can put both versions on to the same item and laugh at every spell/dragon breath tossed in your direction.

It doesn't matter how expensive, effective or powerful the enchantment on the item is. You learn the same enchantment by destroying a 10% sneak item as you do by destroying a 45% item.

As Thaumajig said, the actual enchanting is down to your skill and the items used.