Mahmud I was the first to modernize the Ottoman army during the 1730s, during which the Ottomans received payment of a debt from Sweden in the form of 16,000 muskets as well as explosives. He also brought in a French officer, Claude-Alexandre de Bonneval, to modernize the army. He created musket factories, powder factories, cannon foundries, and a military engineering school.

Then Selim III, in the late 1700s, attempted to further modernize the army. From Osman's Dream: the History of the Ottoman Empire by Caroline Finkel on page 390:

...in 1792, he [Selim III] reviewed the reports on the state of the empire...mainly concerning measures to improve the performance of the Ottoman army in its struffle with Europe - and with Russia in particular. Traditional values, the essayists acknowledged, must be adapted so that the Ottomans could take advantage of modern methods and technology.

With French assistance, especially with that of Francois Baron de Tott, the Ottomans planned an "entirely new body of troops funded by its own treasury." Recruitment for the "New Order', or Nizam-ı Cedit, begain in 1793. Also built was a howitzer foundry.

They attained initial success, defeating an army of Napoleon's in Syria in 1799 with only 500 men. This resulted in its rapid expansion, achieving a size of "more than 22,500 men and 1,500 officers" by 1806.

The Janissaries, the traditional Ottoman army, didn't like this. They had a history of opposing military reforms, and killed sultans as a result of attempts of anything like the formation of a new army. They killed Osman II for what they feared to be his attempts at the creation of a parallel army. This was no different. They rebelled, ultimately defeated the New Order troops, and ousted Selim III.

So, to answer your question, the Ottomans lagged a little behind the military tech of Western Europe due to conservative resistance both politically, and from the existing military. After French assistance, however, they did manage to eventually modernize and were on pace with Western Europe around the mid 1700s and then again at the beginning of the 1800s.

Source:

Osman's Dream: The History of the Ottoman Empire by Caroline Finkel