Sometimes, having two nominally equally equipped armies won't mean stalemate; or defense being the 'superior' mode of warfare: such Clausewitzian ideas of warfare are not considered so absolute - the idea of maintaining the initiative is often the key to success - be it on the offensive, or defensive. Dictating the terms of the battle (and yes, even a defender can do this (e.g: Waterloo)) is often the most important - fighting a battle on your terms is one of the keys to success.

An earlier question asked why France fell so rapidly in Spring 1940. I can think of no better example of what you are looking for - two nominally (keyword: nominally) equal sides fight - one firmly on the defensive, both sides with similar amounts of industrial capability and material available to them.

The key is understanding the employment of their relatively similar equipment.

PS: This will probably get pulled down for the 'throughout history' rule; I'd rephrase and narrow the era.

Within the limits of the question, if I've understood it correctly, I'd point to the Franco-Prussian War of 1870 as an interesting example. This was a case of a clash between two roughly technologically comparable forces in which the offence nonetheless dominated.

In this conflict, when thrown on the defensive the French riflemen (with their excellent chassepots) proved exceptionally effective on the defence. In situations where the French were well entrenched or occupied the high ground (eg Gravelotte–St. Privat) their rifle fire proved devastatingly effective in countering the German infantry.

Unfortunately this advantage in small arms was more than compensated for by the effectiveness of the Prussian artillery. Time and time again the range, accuracy and rate of fire of these guns proved decisive on the battlefield.

Would the war have ended differently if the Germans had possessed inferior artillery? Maybe. But certainly these guns gave the attackers an immense advantage.

(It's also worth looking at the Italian War of 1859 for the exceptionally aggressive French tactics, the so-called Furia francese, that overwhelmed the Austrians. But this I know less about.)

I would argue that the late-war German Stosstruppen units, using infiltration tactics and squad level coordination of heavy weapons and artillery were a case where tactics and weapons outweighed the defensive. The Stosstruppen were specially armed (artillery Lugers, Bergmans, carbines, different bayonets, etc.) to be more maneuverable and effective in the close confines of a trench. They were trained to move in small groups and individual leaders at the squad and platoon level were encouraged to use individual imitative. They also were taught to bypass strongpoints and continue the attack against weaker positions, leaving the stronger portions to second wave troops. The idea was to not have a giant grand plan of miles and miles of rolled up enemy trenches, but to rather punch a hole in a small section and then take advantage of this breach.

I suspect this sub has folks more educated on this than I, not my specialty, I hope one of them chimes in to expand/make corrections.